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I'm trying to solve the above differential equation using the shooting method. When i set Method -> {"Shooting", "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1} i get a solution, but it is equal to zero. I need a solution that is different of zero. When i increase the value of z'[t], say to z'[t]=1000 Mathematica stay running for a long time and i get no solution. How can i solve this?

Here is the code:

n = 3.;
xf = 10000.;
s = NDSolve[
   {
    -z''[t] == (1 + (n - 2) t)^(1/(2 - n) (2 (n - 1) + 0.001)) z[
        t]^2 (Sin[z[t]+2])
    , z[0] == 0, z'[xf] == 0}, z, {t, 0, xf},
   Method -> {"Shooting", 
     "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1}
     }
   ] // Chop
Plot[Evaluate[z[t] /. s], {t, 0., 10}, PlotRange -> All]

I'm trying to solve the above differential equation using the shooting method. When i set Method -> {"Shooting", "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1} i get a solution, but it is equal to zero. I need a solution that is different of zero. When i increase the value of z'[0], say to z'[0]=1000 Mathematica stay running for a long time and i get no solution. How can i solve this?

Here is the code:

n = 3.;
xf = 10000.;
s = NDSolve[
   {
    -z''[t] == (1 + (n - 2) t)^(1/(2 - n) (2 (n - 1) + 0.001)) z[
        t]^2 (Sin[z[t]+2])
    , z[0] == 0, z'[xf] == 0}, z, {t, 0, xf},
   Method -> {"Shooting", 
     "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1}
     }
   ] // Chop
Plot[Evaluate[z[t] /. s], {t, 0., 10}, PlotRange -> All]

I'm trying to solve the above differential equation using the shooting method. When i set Method -> {"Shooting", "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1} i get a solution, but it is equal to zero. I need a solution that is different of zero. When i increase the value of z'[t], say to z'[t]=1000 Mathematica stay running for a long time and i get no solution. How can i solve this?

Here is the code:

n = 3.;
xf = 10000.;
s = NDSolve[
   {
    -z''[t] == (1 + (n - 2) t)^(1/(2 - n) (2 (n - 1) + 0.001)) z[
        t]^2 (Sin[z[t]] + 2)
    , z[0] == 0, z'[xf] == 0}, z, {t, 0, xf},
   Method -> {"Shooting", 
     "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1}
     }
   ] // Chop
Plot[Evaluate[z[t] /. s], {t, 0., 10}, PlotRange -> All]

I'm trying to solve the above differential equation using the shooting method. When i set Method -> {"Shooting", "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1} i get a solution, but it is equal to zero. I need a solution that is different of zero. When i increase the value of z'[t], say to z'[t]=1000 Mathematica stay running for a long time and i get no solution. How can i solve this?

Here is the code:

n = 3.;
xf = 10000.;
s = NDSolve[
   {
    -z''[t] == (1 + (n - 2) t)^(1/(2 - n) (2 (n - 1) + 0.001)) z[
        t]^2 (Sin[z[t]+2])
    , z[0] == 0, z'[xf] == 0}, z, {t, 0, xf},
   Method -> {"Shooting", 
     "StartingInitialConditions" -> {z[0] == 0, z'[0] == 1}
     }
   ] // Chop
Plot[Evaluate[z[t] /. s], {t, 0., 10}, PlotRange -> All]